Magic Squares of Odd Orders Mystery Cache

A magic square is a grid of numbers where the numbers in each row, column and the two main diagonals sum up to the same value.

This cache is the first in a series of three which will, when completed, show you how to create magic squares of any number of cells per side.

This cache will show you how to create magic squares of an odd order, which means that the count of numbers in each row or column of the square is the same odd number (1, 3, 5, 7, etc.).

The other two caches in the series show you how to create squares of even orders. The second cache in the series shows you how to create squares of a doubly even (divisible by 4) order (4, 8, 12, etc.), and the third cache in the series shows you how to create squares of a singly even (not divisible by 4) order (6, 10, 14, etc.). There is no magic square of order 2. Solving this first cache is a prerequisite to solving the third cache in this series, as the techniques used to build magic squares of a singly even order will build on methods learned here.

The cache itself is a camouflaged plastic candy tube, with a rounded (half-sphere) black lid on either end. A gift of Marky and Joani, it contains a log sheet and a pen, as well as assorted small trade items.

Examine the 7x7 square shown below. Once you’ve detected a pattern in the way the numbers are placed in the square, you should find it easy enough to create either 3x3 or 5x5 magic squares. Try that.

Once you’re certain that you’ve figured out how to build 3x3, 5x5 and 7x7 squares, you should be able to tackle the big 15x15 square. We’ve filled in some of the numbers to help you check your work. When you’ve completed the square, take the values in the yellow squares and concatenate them to form the latitude and longitude of the cache.

You will be teaching yourself the “De la Loubere method” for constructing magic squares. De la Loubere visited Siam on behalf of King Louis XIV of France. He learned this method of magic square construction while stationed there.

Note: It is possible to create multiple valid 15x15 squares. However, you’re looking for one that follows the pattern shown in the 7x7 magic square.

Note: Any log that gives hints about the location will be deleted. Each cache in the series will be at a different location. This location was chosen in a brief fit of silliness, and will best be appreciated if you have solved other puzzle caches in the Bay Area.